MAKING INFERENCES CONFIDENCE INTERVALS CALCULATING CONFIDENCE INTERVALS The

MAKING INFERENCES

CONFIDENCE INTERVALS •

CALCULATING CONFIDENCE INTERVALS The confidence interval can be found using straight forward substitution (but you will need your summary statistics handy) Eg. Find the informal CI for the male sample. IQR = 21 (171 – 150) n=42 median=161 (be careful not to use mean!!!) So my informal confidence interval for male armspans is between 156 and 166 cm. 156 cm 166 cm

DESCRIBING WHAT THE INTERVALS ARE 2200 2050 3700 3950 The informal confidence interval is useful because if I took samples again and again the population median (not the sample median) is likely to lie in it most of the time. I am pretty sure that the [median] [bag weight] for [males] in [NZ] is between 2200 and 3700 g and the [median] [bag weight] for [females] in [NZ] is between 2050 and 3950 g

THE INFERENCE (MAKING THE CALL) To make a call from the Informal Confidence Interval we consider whether or not they overlap. Essentially, it’s a yes/no question 1) NO: the informal confidence intervals do not overlap. Therefore I can make the call that back in the population the [median] [wrist size] of [males] at [mount albert Grammar School] is bigger than the [median] [wrist size] of [females] at [Mount Albert Grammar School]. 2)YES: the informal confidence intervals do overlap. Therefore I cannot make the call that back in the population the [median] [armspan] of [left handed] students at [Mount Albert Grammar School] is bigger from the [median] [armspan] of [right handed] students at [Mount Albert Grammar School]

• When you make a call, it should include the same four things that featured in the question (statistic, variable, group, population) • If any of these four are missing you will fail. So please look at the examples again, notice the bits in square brackets, you cannot afford to miss even one of these…

THE INFERENCE (MAKING THE CALL) To make a call from the Informal Confidence Interval we consider whether or not they overlap. Essentially, it’s a yes/no question 1) NO: the informal confidence intervals do not overlap. Therefore I can make the call that back in the population the [median] [wrist size] of [males] at [mount albert Grammar School] is bigger than the [median] [wrist size] of [females] at [Mount Albert Grammar School]. 2)YES: the informal confidence intervals do overlap. Therefore I cannot make the call that back in the population the [median] [armspan] of [left handed] students at [Mount Albert Grammar School] is bigger from the [median] [armspan] of [right handed] students at [Mount Albert Grammar School]

YOU MUST CORRECTLY CHOOSE WHETHER OR NOT TO MAKE A CALL FOR ACHIEVED (AFTER ALL, THE STANDARD IS CALLED INFERENCE) FOR MERIT, THIS SHOULD BE ACCOMPANIED WITH A DESCRIPTION OF WHAT THE INTERVAL ARE AND WHAT THEY REPRESENT I SHOWED THIS EARLIER (AGAIN, WE NEED TO SHOW AN UNDERSTANDING THAT WE ARE CONSIDERING THE POPULATION WHEN TALKING ABOUT THE INFORMAL CONFIDENCE INTERVALS)

DESCRIBING WHAT THE INTERVALS ARE 2200 2050 3700 3950 • The informal confidence interval is useful because if I took samples again and again the population median (not the sample median) is likely to lie in it most of the time. • I am pretty sure that the [median] [bagweight] for [males] in [NZ] (population) is between and 2200 and 3700 g and the [meidan] [bagweight] for [females] in [NZ] (population) is between 2050 and 3950 g

NOW YOU TRY IT

2200 2050 3700 3950

2200 2050 3700 3950 Write a conclusion • From my confidence intervals, I am pretty sure the median bagweight of males at MAGS is between 2200 g and 3700 g and the median bagweight for females at MAGS is between 2050 g and 3950 g. • The informal confidence interval is useful because if I took samples again and again the population median bagweight is likely to lie in it most of the time. • The informal confidence intervals do overlap. Therefore I cannot make the call that back in the population the median bagweight of boys at Mount Albert Grammar School is bigger than the median bagweight of girls at Mount Albert Grammar School

Write a conclusion • From my informal confidence intervals, I am pretty sure the median height of backs in the All Blacks and Springboks is between 1. 81 m and 1. 83 m and the median height forwards in the All Blacks and Springboks is between 1. 88 m and 1. 91 m. • The informal confidence interval is useful because I took samples again and again the population median height is likely to lie in it most of the time. • The informal confidence intervals do not overlap. . Therefore I can make the call that back in the population the median height of forwards in the All Blacks and Springboks are taller than the median height of backs in the All Blacks and Springboks